Is it permissible for an employee to take the transportation allowance and record it among his expenses, if he rides with another person out of courtesy, and does the ruling differ if the person doing the favor expects a return favor or not, and is it permissible to take a separate fare for each employee when jointly renting a car?

If the transportation allowance allocated to employees is disbursed to them as an act of ownership (تمليك), then it becomes their established right, regardless of their mode of transport. However, if the employer provides transportation or only reimburses for actual expenses, then the employee is only permitted to claim what they have actually spent. It is not permissible for the employee to defraud the company by taking money unlawfully.